Module 5: Sampling Distributions & Hypothesis Testing

Module 5 looks closely at inferential statistics and what all goes into hypothesis testing.

Learning Objectives

These are the learning objectives for this portion of the class:

  1. Define inferential statistics
  2. Graph a probability distribution for the mean of a discrete variable
  3. Describe a sampling distribution in terms of “all possible outcomes”
  4. Describe a sampling distribution in terms of repeated sampling
  5. Describe the role of sampling distributions in inferential statistics
  6. Define the standard error of the mean
  7. State the mean and variance of the sampling distribution of the difference between means
  8. Compute the standard error of the difference between means
  9. Compute the probability of a difference between means being above a specified value
  10. State how the shape of the sampling distribution of r deviates from normality
  11. Transform \({r}\) to \({z}'\)
  12. Compute the standard error of \({z}'\)
  13. Calculate the probability of obtaining an r above a specified value
  14. Compute the mean and standard deviation of the sampling distribution of \(p\)
  15. State the relationship between the sampling distribution of p and the normal distribution

These are the learning objectives for this portion of the class:

  1. Describe the logic by which it can be concluded that someone can distinguish between two things
  2. State whether random assignment ensures that all uncontrolled sources of variation will be equal
  3. Define precisely what the probability is that is computed to reach the conclusion that a difference is not due to chance
  4. Define “null hypothesis”
  5. Define “alternative hypothesis”
  6. Describe how a probability value is used to cast doubt on the null hypothesis
  7. Define “statistically significant”
  8. Define Type I and Type II errors
  9. Explain why the null hypothesis should not be accepted when the effect is not significant
  10. State what it means to accept the null hypothesis
  11. Discuss the problems of affirming a negative conclusion
  12. Be able to state the null hypothesis for both one-tailed and two-tailed tests
  13. Differentiate between a significance level and a probability level
  14. State the four steps involved in significance testing
  15. Determine from a confidence interval whether a test is significant
  16. State why the probability value is not the probability the null hypothesis is false
  17. Explain why a low probability value does not necessarily mean there is a large effect
  18. Explain why a non-significant outcome does not mean the null hypothesis is probably true

Consumables

Each week there will be a number of items for you to consume, be it reading, watching, listening, or a combination thereof.

Consumable materials for module grouped by required or supplemental content.
Module Required? Text/Resource Chapter/Title Estimated time in minutes Type
5 Required Online Statistics Textbook Chapter 9: Sampling Distributions 120 Mathematics
5 Required Online Statistics Textbook Chapter 11: Logic of Hypothesis Testing 120 Mathematics
5 Supplemental Manga Guide to Statistics Pages 89-98, 143-189 90 Mathematics
5 Supplemental Introductory Statistics Sampling Distributions 10 Mathematics
5 Supplemental Introductory Statistics Hypothesis Testing 10 Mathematics
5 Supplemental 365 Data Science Type I error vs Type II error 4 Mathematics
5 Supplemental Crash Course Statistics The Shape of Data: Distributions 12 Mathematics
5 Supplemental Crash Course Statistics Probability Part 1: Rules and Patterns 12 Mathematics
5 Supplemental Crash Course Statistics Probability Part 2: Updating Your Beliefs with Bayes 12 Mathematics
5 Supplemental Crash Course Statistics The Normal Distribution 12 Mathematics
5 Supplemental Crash Course Statistics Confidence Intervals 13 Mathematics
5 Supplemental Crash Course Statistics How P-Values Help Us Test Hypotheses 12 Mathematics

The total amount of time estimated on required texts and resources is 240 minutes, while you should expect to spend at most an additional 187 minutes on supplemental material.

The total amount of time estimated you should spend on these assignments depends on the amount of effort required, itself based on your previous experience with statistics, generally, and R, in particular. You can expect to spend somewhere between 96 and 287 minutes on this module beyond the readings. The estimated total number of words you’re likely to write in this module is 1,250.

Assignments for this module.
Module Due date Assignment type Short name Long name Points Effort (low) Effort (high) Expected word total
5 2024-02-16 Questions CH9M Chapter 9 questions 3 6 12 125
5 2024-02-16 Questions CH11M Chapter 11 questions 3 5 10 125
5 2024-02-16 Quiz CH9Q Chapter 9 quiz 15 10 45 0
5 2024-02-16 Quiz CH11Q Chapter 11 quiz 15 15 40 0
5 2024-02-16 Activity AD Activity D: Research 20 60 180 1,000

Module 5 Activity

This module’s activity covers research.

Quiz

Don’t forget about your chapter quizzes! Find them in the Quizzes menu in D2L.

Chapter Questions

Each week’s chapters follow the same basic process but may be slightly different in terms of which questions you can and cannot choose from. Be sure to read the instructions carefully!

Steps to completion

  1. (Setup: create your copy of the Chapter Questions Posit Cloud project once it’s available. Inside you will find a document template for creating your submitted responses.)
  2. From the end-of-chapter exercises for each chapter, choose three questions from the provided list.
  3. Do not choose from the “Questions from Case Studies” section.
  4. Create a Quarto HTML document using the provided template and answer the questions. This is an opportunity to practice your formatting and information presentation skills as many questions require varied approaches to response.
    1. Be absolutely certain that you leave the embed-resources: true YAML key present! Otherwise, the HTML file you submit will likely break anywhere other than your project.
  5. Submit your rendered HTML file (one per module) to the relevant module’s “Participation” dropbox.
    1. For example, in the Module 1 Exercises dropbox you should upload a single document for Chapter 1 questions and responses, and your Chapter 6 questions and responses.
    2. You will need to make sure your files are named appropriately by changing the output-file YAML key. Your template has instructions to remind you of this.

You are only required to do 3 questions in total.
Make sure to indicate the chapter and question that you are answering in your answer document.

Chapter 9, choose from: 4-10, 15, 16

Chapter 11, choose from: any except 20-24